arXiv subjects

Elvira Di Nardo

Publications and source records attributed to Elvira Di Nardo.

21 records · Page 2Linked to original sources

arXiv2008

A unifying framework for $k$-statistics, polykays and their multivariate generalizations

Through the classical umbral calculus, we provide a unifying syntax for single and multivariate $k$-statistics, polykays and multivariate polykays. From a combinatorial point of view, we revisit the theory as exposed by Stuart and Ord, taking into account the Doubilet approach to symmetric functions. Moreover, by using exponential polynomials rather than set partitions, we provide a new formula for $k$-statistics that results in a very fast algorithm to generate such estimators.

math.CO↗

arXiv2007

On certain bounds for first-crossing-time probabilities of a jump-diffusion process

We consider the first-crossing-time problem through a constant boundary for a Wiener process perturbed by random jumps driven by a counting process. On the base of a sample-path analysis of the jump-diffusion process we obtain explicit lower bounds for the first-crossing-time density and for the first-crossing-time distribution function. In the case of the distribution function, the bound is improved by use of processes comparison based on the usual stochastic order. The special case of constant jumps driven by a Poisson process is thoroughly discussed.

math.PR↗

arXiv2004

Simulations of Gaussian Processes and Neuronal Modeling

The research work outlined in the present note highlights the essential role played by the simulation procedures implemented by us on CINECA supercomputers to complement the mathematical investigations carried within our group over the past several years. The ultimate target of our research is the understanding of certain crucial features of the information processing and transmission by single neurons embedded in complex networks. More specifically, here we provide a bird's eye look of some analytical, numerical and simulation results on the asymptotic behavior of first passage time densities for Gaussian processes, both of a Markov and of a non-Markov type. Several figures indicate significant similarities or diversities between computational and simulated results.

math.ST↗